Middle-class families have moved into neighborhoods such as Columbia Heights and Petworth in large numbers. And many of these families are staying in the District even after their kids are old enough to attend school.

Meanwhile, more parents in D.C. neighborhoods west of Rock Creek Park are sending their kids to public schools, resulting in fewer spots for “out of boundary” students in the most sought-after neighborhood schools such as Lafayette, Murch and Eaton elementary schools or Deal Middle School.

As a result, more-affluent parents in the transitioning neighborhoods — squeezed out of schools west of the park and unable to afford private schools — are taking a shot at either the elementary school down the street or a diverse charter school nearby. In several cases, this has been an orchestrated effort, organized via community meetings or e-mail discussion groups. The trend is particularly pronounced in both district and charter preschool programs, resulting in class rolls that are much more diverse than those in the upper grades.

If you believe that the overall value of a community is enhanced when it can support high-quality, integrated schools, these shifts mark a significant development for the city. There are plenty of reasons to cheer school integration beyond promoting Dr. Martin Luther King Jr.’s powerful dream of creating a multiracial “beloved community.” Evidence shows that poor and rich kids benefit when they attend integrated schools. Indeed, researchfinds that students of all backgrounds experience civic, social and cognitive benefits from learning in diverse settings — benefits that are increasingly important as students prepare to enter an economy that values critical thinking, collaboration and creativity.

But these changes are not without their challenges. At some D.C. elementary schools, rather than settling into a healthy racial and socioeconomic balance, student populations are flipping from one extreme to the other, with fourth-grade classes dominated by minorities and preschool classes that are mostly white.

At these rapidly changing schools, mostly white, middle- and upper-middle-class families are pushing out poor or working-class “out of boundary” minority families. Many of these middle-class parents want their schools to remain diverse, and lower-income families want to be a part of these successful schools. Yet both are powerless to keep this Big Flip from happening.

Even some charter schools — which don’t have “in boundary” families — may face kindred challenges as they gain popularity among more affluent families. Because charter schools in the District generally are required to select students via a blind (unweighted) lottery, the more affluent parents who apply, the more who are likely to get in.

We can do better. Here’s how:

The first strategy we propose is to create controlled-choice zones in strategic parts of the city (namely, Capitol Hill, Columbia Heights, Mount Pleasant, Adams Morgan, Dupont/Logan Circle and Petworth). In these neighborhoods, school attendance zones would eventually go away, as they have in a number of other districts across the country that use the controlled-choice model. Parents would express preferences among a cluster of schools, and an algorithm would make matches by balancing personal preferences with the shared civic goal of maximizing socioeconomic integration. Ideally, this list of options would include both district schools and public charter schools. Neighborhood schools in these zones that are disproportionately low-income would be reformed as magnet schools with attractive educational programs and themes to appeal to more middle-income families. Because all of the school options would be in the general neighborhood, no one would be forced to trek across town.

The second strategy we propose is to allow public charter schools and magnet schools to use weighted lotteries to create or maintain socioeconomic diversity. With a weighted lottery, charter schools could ensure that their proportion of poor students served never drops below 50 percent, even if a large number of middle-class families enters the lottery.

The D.C. Advisory Committee on Student Assignment has the opportunity to shape school enrollment patterns in the city in this pivotal time of demographic change. We encourage the committee to include policies that preserve and promote socioeconomically integrated options for families in their recommended strategies and guidelines for student assignment and school choice.